A185167 Primes of the form k*6^m +1 where k is a Mersenne prime (A000668) and m is an integer.

19, 43, 109, 1117, 3889, 40177, 139969, 326593, 839809, 4718557, 5038849, 5925313, 18874333, 52068097, 1088391169, 1874451457, 6115248577, 24461134273, 1410554953729, 2429289086977, 31701630016513, 118486616113153

Offset: 1

Author

Gilbert Mozzo, Feb 18 2011

Keywords

• nonn

Examples

			(2^521-1)*6^959+1 is prime
		

Crossrefs

Cf. A000668, A185069.

Programs

Magma

// For the Mersenne prime 2^521-1, for example:
[n: n in [0..1000] | IsPrime((2^521-1)*6^n+1)];

Mathematica

Union[Flatten[Table[Select[p*6^Range[0, 30] + 1, # < 10^20 && PrimeQ[#] &], {p, {3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951}}]]]
Union[Flatten[Table[Select[(2^MersennePrimeExponent[n]-1)6^Range[ 0,20]+ 1,PrimeQ],{n,20}]]] (* Harvey P. Dale, Aug 15 2021 *)

Extensions

Partially edited by N. J. A. Sloane, Feb 19 2011